Sorting by absolute value without changing the data

UPDATE

Since 0.17.0 order and sort have been deprecated (thanks @Ruggero Turra), you can use sort_values to achieve this now:

In[16]:

df.reindex(df.b.abs().sort_values().index)
Out[16]: 
   a  b
2  3 -1
3  4  2
0  1 -3
1  2  5
4  5 -9